Roof construction

ABSTRACT

A roof structure having a peripheral support ring is disclosed wherein the ring comforms in plan substantially to a closed curve having major and minor axes and at least two skewed axes of symmetry. A plurality of sets of arches are connected to the ring to form the roof, with the arches of at least two sets respectively extending in plan substantially parallel to a separate one of the skewed axes of symmetry of the closed curve and the arches of another set extending in plan substantially parallel to the major and/or the minor axes of the closed curve. The arches impose a funicular load on the ring and support a roof deck structure to form a dome surface.

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ate 1191 [111 3,341,038

[ Uct. 15, 1974 [5 R001 CONSTRUCTIION 484,435 5/1925 Germany 52 86 415,870 7/1925 G 52 86 [76] Inventor: David H. Geiger, 788 R1vers1de Dr., 1,185,792 H1965 New York, 10032 197,921 7/1967 U.S.S.R 52/83 [22] Filed: May 11, 1973 Primary Examiner-John E. Murtagh Assistant Examiner--l-lenry Raduazo Attorney, Agent, or Firm-Curtis, Morris & Safi'oro Appl. 196.; 359,553

Related US. Application Data Division of Ser. No. 133,198, April 12, 1972, Pat. No. 3,772,836, which is a continuation-in-part of Ser.

No. 80,048, Oct. 12, 1970, [57] ABSTCT 52] 11.5. c1. 52/80 52/167 A structure having a Peripheral Support ring is 51 11m. (:1 ..E(14b 1/32 E6415 1/36 disclOsed wherein the ring Comforms in P Substan- [58] Field M Search 52/2 80 SI 83 167 tially a closed curve having major and minor axes and at least two skewed axes of symmetry. A plurality 5 References Cited of sets of arches are connected to the ring to form the roof, with the arches of at least two sets respectively UNITED STATES PATENTS extending in plan substantially parallel to a separate 3,077,961 2/1963 De1cke 52/81 one of h skewed axes of Symmetry of the closed 1 g l 25 curve and the arches of another set extending in plan 3540174 1151970 2, substantially parallel to the major and/or the minor 3'744191 7/1973 Bird axes of the closed curve. The arches impose a funicu- 3:757:478 9 1973 Pryor 52/80 lar load the ring and PP a roof deck Structure 1: f cl rf FOREIGN PATENTS OR APPLICATIONS a ace 1,191,776 2/1958 France 52/81 14 Claims, 8 Drawing Figures 213 1 9 we I I g 2. a 1 1 a 2 t? I I 1 I g PATENTED W 1 51974 SHEET 1 BF 5 fwd/M AX/S F/GZ noor comsrnucrrou This is a division, of application Ser. No. 133,198, filed Apr. 12, 1971 now U.S. Pat. No. 3,772,836 which is a continuation-in-part of co-pending United States Patent Application Ser. No. 80,048 (CMS File No. 185055), filed Oct. 12, 1970 the disclosure of which is incorporated herein by reference. This invention relates to a roof construction, and more particularly to a domed roof structure including a peripheral structural ring which restrains the remaining elements of the roof.

In dome roof constructions wherein the roof is supported only the structural members forming the dome, without the use of interior columns or beams, it is desirable to control the nature of forces in the structural ele ments of the dome so that each of the structural elements carry nearly the same load and may be formed of the same size structural member, or so that joint details, particularly where the joint is formed of wood, may be readily solved for transmission of bearing forces therethrough.

The dome of the present invention accomplishes these and other ends by utilizing a peripheral ring and structural elements such as rigid arches, which are connected to the ring in a predetermined pattern such that the ring is loaded in a substantially funicular manner. The configuration of the ring is selected from the family of closed curves having major and minor axes and at leastxtlwo skewed axes of symmetry (more fully described ereinafter) and a plurality of sets of arches are secured to the ring for supporting the roof deck structure. Two of the sets of arches are respectively positioned parallel to the skewed axes of symmetry of the ring and a third set of arches are located in plan substantially parallel to the major or minor axes of the ring and pass through the vertices of the diamond shaped pattern generated by the first two sets of arches. In this manner the framing system for the rigid structure is triangulated, except possibly at the ring. Triangulation at the ring is accomplished, if desired, by slight changes in directions of one or more of the arches adjacent the ring, to enhance structural stability of the dome.

The above, and other features and advantages of this invention, will be apparent in the following detailed description of illustrative embodiments thereof which are to be read in connection with the accompanying drawings, wherein:

FIG. l is a diagram of a closed curve to which the ring of the roof structure of the present invention may conform and illustrates certain properties of that curve useful in explaining the invention;

FIG. 2 is a diagram showing the family of superellipses (x/a) (y/b) l, with aa b but of the same values for each ellipse shown and with m passing through values (including non-integral values) from less than unity up to infinity, for which latter value the ellipse takes the form of a rectangle circumscribing all ellipses of the family;

FIG. 3 is a schematic plan view of a roof construction according to the invention;

FIG. 4 is a force diagram of a portion of the structure shown in FIG. 3;

FIG. 5 and 6 are'schematic plan views of other roof structures constructed according to the present invention;

FIG. 7 is a sectional view taken along line 77 of FIG. 6 illustrating the foundation support of the ring for ring a roof structure constructed in accordance with the present invention; and

FIG. 8 is a sectional view taken along line 8-8 of FIG. 7.

Referring to the drawings in detail, and initially to FIG. 1 thereof, there are illustrated two lines M and N which are not perpendicular and which are axes of skewed symmetry for the closed curve 110, since any line L intersecting one of these axes (for example, line L intersecting axis N at B) which is parallel to the other axis (M) intersects the curve 110 at points C and A such that the distance AB is equal to the distance BC. Curves illustrating this characteristic are referred to herein as curves having skewed axes of symmetry. There are numerous curves having this characteristic and the curve 10 illustrated in FIG. I, which is shown by way of example is an ellipse conforming to the usual equation A family of closed curves which has skewed axes of symmetry, thereby having the characteristic of skewed symmetry as referred to hereinafter, is the family of ellipses and superellipses generated by the equation (x/a)" (y/b) 1, some of which are shown in FIG. 2. Whatever the value of m, the ellipse can be circumscribed with a rectangle whose sides are perpendicular to the major and minor axes of the ellipse, with the rectangle being tangent to the ellipse at the intersections of the major and minor axes thereof. It is a property of this family of curves that the diagonals 114 and 116 of the circumscribing rectangle 12 are their axes of skewed symmetry, whatever the value of m. This may be demonstrated by a coordinate transformation to the i1: and 1 axis where x (1 ll!) cos a,y ('n ll!) cos a, and a tan b/a.

In these expressions, illustrated with reference to FIG. 2, a is theangle between the major axes of the ellipses of that figure and the adjacent diagonal of the circumscribing rectangle l2. 1 is the length measured along the direction of diagonal 16 as a slant coordinate axes, and III is the length measured along the diagonal 14 of the circumscribing rectangle as another slant cordinate axis.

In accordance with the present invention, structural members forming the dome or roof construction are placed so as to project in plan as straight lines parallel to the axes of skewed symmetry of the closed curve. Such as for example, the axes of MI and N of the ellipse of FIG. 11 or the axes I41 and 16 of the family of ellipses and super-ellipses illustrated in FIG. 2. The structural members of the present invention are rigid arches which provide the roof framing structure. With the structural members of the dome positioned in this manner and connected to a peripheral ring conforming, or substantially conforming to a closed curve having the property of skewed symmetry, the invention provides a roof structure wherein the ring is substantially free of bending moments in the horizontal plane and is to that extent funicular. This is achieved by selecting the ordinates of the respective arches such that the horizontal component of forces therein, as a result of the roof loads which they must support, impose at their connection with the ring forces which load the ring in a substantially funicular manner.

One roof construction according to the invention is shown in FIG. 3, wherein a ring 18 of elliptical shape rests upon a suitable foundation 20 of concrete or the like, having the same outline as the ring. Two sets of interconnected arches 22 and 24 are provided with the arches of each set respectively extending parallel, in projection, onto the horizontal plane, to one of the diagonals 14 or 16 of the circumscribing rectangle 12. These arches carry the uniform roof load to the ring and apply substantially equal horizontal components of force to the rings at their opposed ends. Another set of arches 26 are provided in the dome construction of the present invention which may extend parallel to the major or minor axes 30 and 28 respectively, and which are adapted to carry the unsymmetric and/or antisymmetric loads for which the roof structure is designed. In the preferred embodiment of the present invention, as illustrated in FIG. 3, the third set of arches 26 are positioned to extend parallel to the minor axes of the closed curve 10. The arches support a roof decking system (not shown) including purlins extending between the arches for supporting the roof covering member, which may be of conventional construction, and which forms the domed surface of the roof structure.

The ordinate location and arrangement of the arches is selected methematically so as to control the magnitude and character of the forces within the arches and ring and to provide the roof shape desired. For example, if, as in FIG. 3, the arches are in two sets 22 and 24 of equally spaced arches parallel to the diagonal axes l4 and 16, the horizontal components of force to be exerted by each arch at its point of connection with the ring 18 can be evaluated in terms of the stress along the ring, i.e. tangent to the axis of the ring, at the intersections of the diagonals l4 and 16 with the ring. The ring will obviously be in tension in the completed roof structure and the tensile stress denoted P, initially selected for the ring on the assumption that the arches 22 and 24 are in compression. With P acting at E and F being the internal force in the ring, let the horizontal component of the arch reactions I-l, acting on the ring segment EF (which extends from the intersection of diagonal 16 with the ring at E past the intersection therewith of the major axis 30 to the intersection therewith at F of the other diagonal 14) be as shown in FIG. 4. By considering the equilibrium of ring segments of the free body EF from E to H E to H etc., the horizontal reactions H H etc. can be determined in terms of P. Similarly, if there is considered the ring segment DE between the intersection of the ring at D of the opposite end of diagonal l4 and the point E already defined, and if there is determined the relationship between the horizontal component H and the force P, one finds that the opposite ends of each arch in the set 24 acting on ring segment EF exert the same horizontal reaction on the ring segment DE. The remaining corresponding segments of the ring may be similarly analyzed and it is found that the opposite ends of each of the arches in both sets 22 and 24., exert the same horizontal reaction 'on the ring. Thus, the horizontal component of the forces in the arches required to funicularly load ring 18 are determined in terms of the selected force P.

With the horizontal components of the forces in the arches at their points of connection to ring 18 thus determined as a function of the axial force P in the ring at its intersection with the diagonals l4 and MS, a suitable shape for the roof in terms of the rise of the roof above the plane of the ring and the consequent configuration of the arches themselves can be arrived at by considering vertical equilibrium at each of the intersections of the arches. The material of the roof and accessory elements such as the arches themselves and the symmetric live load being known, the weight per unit projected area of the roof dome can be estimated. This gives the vertical force to be supported at the arch intersections (roof joints), and this vertical force with an assumed value of P, can be utilized to compute the vertical ordinates of the arches at the various joints necessary for the stresses in the arch to have this vertical resultant and to have simultaneously the desired horizontal component at the points of connection of the arches with the ring. If the resultant three-dimensional shape of the roof is not the one desired, another value of the axial ring stress P can be assumed and another shape can be computed for the roof by the same process. In this way there can be found at least two roof shapes on either side of the one desired, for example, as to the degree of convexity thereof and the size of the structural arch members, and extrapolation between the two will yield the desired seape and the required ring force.

The set 26 of arch members is provided in the dome structure in order to add structural stability to the dome under unsymmetric or antisymmetric loads. These arches are positioned in the preferred embodiment of the present invention parallel to the minor axes of the ellipse defined by ring 18 and are connected, as illustrated in FIG. 3, to the arches extending parallel to the skewed axes of symmetry at the vertices of the diamond-shapped pattern generated by the former set of arches. In this manner, the framing system of the roof structure is triangulated, except possibly at the ring itself. However, as more fully described hereinafter, triangulation at the ring may, if desired be accomplished by slight changes of one or more of the arch directions in the neighborhood of the ring.

The arches in sets 22 and 24 are selected and designed to carry the symmetrical loading of the roof. The arches in set 26 with the arches in sets 22 and 24 carry the antisymmetric loadings for which the roof is designed. The relationship between the ring shape, the symmetric roof load and the vertical ordinates of the intersection points of the framing system is established mathematically so as to control the magnitude and size of the forces within the various arch members so that joint details in wooden arch structures may be simplifled and/or so that the arches in steel arch dome structures carry nearly the same load and may be formed of the same sized structural members for economy in constructing the roof.

For example, the roof ordinates may be established so that the two sets of arches 22 and 24 extending parallel to the axes of skewed symmetry are in compression under the symmetric roof loads and for certain ring shapes and loading these compressive forces may be nearly equal and of comparatively large magnitude. Under the symmetric loading case, the third set of arches 26 will have nearly zero loads. For antisymmetric loads, which are combined with the symmetric loading to determine the structural design loads (for example full snow load on the other half of the structure) it is found that the two sets or arches orginally in compression are still in compression. Thus, for the wooden arched structures, these arches may be made discontinuous at a joint since the compression forces can be transmitted through joint structures in wooden arch construction in bearing and shear. This permits the other set of arches 26, which are designed to carry the antisymmetric loads, and which may be in tension, compression, or bending, to be continuous through the joint, since in wood joint constructions it is difficult to transmit tensile or bending stresses. Thus, by controlling the nature of forces in the system, a joint detail, particularly, in wood can be readily solved by one skilled in the art. On the other hand, in steel arch constructions, the joints between the arches readily transmit either tensile or compressive forces. Accordingly, the ring shape and roof ordinates may be established such that each of the arch members are under substantially the same stress and carry nearly the same load so that the arches may be formed of the same sized structural members. This results in a substantial economy in constructing the arched dome since the variety of sizes of structural members required for the construction is minimized.

Another closed curve having the property of skewed symmetry, wherein the horizontal forces at the ends of each of the arches extending parallel to the skewed axis of symmetry have the same value so that the peripheral ring to which the arches are connected is funicularly loaded, is illustrated in FIG. 4. The arch structure schematically shown therein is for a wooden arch construction and the diagonals 32 and 34 of the circumscribing rectangle 36 are its axes of skewed symmetry while axes 38 and 48 are its axes of symmetry in the conven tional sense and constitute minor and major axes respectively.

The curve illustrated in FIG. 5 is defined by the set of equations with a and b having given values equal to one-half the lengths of axes 4t and 38 respectively, and the values 0, d, and n arbitrarily selected. The ring 58, having dimensions selected in accordance with the above equations, is arranged to pass through the following coordinates with respect to the major axis 49 (x) and the minor axis 38 (y):

Each of the coordinates defined in this manner locates on ring 50 a joint between the ring and the end of one of the arches extending parallel to the axes of skewed symmetry. By arranging the arches parallel to the skewed axes of symmetry in this manner and with this curve, the ring 50 is funicularly loaded so that it is free of bending moments in its horizontal plane.

it is noted that a curve constructed in accordance with the above equations is also suitable for use with an inflated dome structure similar to that disclosed in my abovementioned copending US. patent application and that the cables in such a dome structure will funicularly load the ring to which they were secured. However, the dome structure illustrated in FIG. 5 has been designed for a wooden arch construction and accordingly, a set of cross-arches 52 extending parallel to minor axes 38 have been provided.

It is noted that the points of intersection of the arches in sets 56 and 58, that is, the vertices of the diamond shaped pattern generated by these intersecting arches are located along imaginary lines extending parallel to the major and minor axes of ring 58. These arches are operatively interconnected at each of these intersections and the latter are located at vertical ordinates with respect to the base, in the manner described above, such that the loading of ring 58 is funicular. Arches 52, provided parallel to minor axis 38, are lo cated along alternate ones of the imaginary joint lines to provide a coarse triangulation within the dome for added stability. Thus, for example, triangulation is provided between joints 68, 82, and 64 by the arch sections 66, 68 and 70 between these joints. Similarly, other joints in the frame are triangularly related to provide triangulation in the roof structure.

As with the previously discussed embodiment, the coarse arches 52 carry the antisymmetrical loads for which the roof structure is designed.

Each of the joint structures in this dome are illustrated by symbols which represent continuity or discontinuity of the respective arches through the joint. Thus, since the arches as and 58 extend parallel to the skewed axis of symmetry and are in compression under substantially all loading conditions, they are formed in segments between the joints because the compressive forces therein are readily transmitted through wood joint constructions. 0n the other hand, the arches in set 52, which carry compressive and tensile loads since they are designed to carry the antisymmetric design loads of the roof structure, are continuous at those joints through which tensile forces must be transmitted. This is advantageous since, as mentioned above, it is difficult to design wood joints for transmitting tensile stresses; Accordingly, the problem is avoided by making the arch continuous through such joints.

it is noted that while a coarse" triangulation has been used in the embodiment of the invention illustrated in FIG. 5, a finer triangulation, that is, a dome structure having cross-arches from set 52 through each of the imaginary lines of joints extending parallel to minor axis 38, may be provided for additional stability against extreme conditions or for larger and heavier roofs. One such embodiment is illustrated in FIG. 6, wherein a dome structure is shown for construction with steel members. The dome therein is constructed in accordance with the same equations and coordinate locations as the previously discussed dome with, however, the arches 52 being located along each of the lines of the joints. Further, in this embodiment the triangulation of the arches has been carried up to ring 50 by deflecting the end portions of certain of the crossarches in set 52. For example, the ends of arches 72, 74-, '76 and 78 have been slightly diverted from positions parallel to minor axis 38 in order to join with an adjacent arch extending parallel to a skewed axis of symmetry at the ring, so that triangulation is carried to the ring. T

in the steel construction such as that illustrated in FIG. 6, wherein compressive and tensile forces may be readily transmitted through the joints between the arches, the ring shape and vertical ordinate of the location of the joints between the arches may be determined, as described above, such that the forces along an individual arch will be substantially euqal and so that the forces within sets of arches will also be substantially equal, whereby all of the arches in a set may be formed of substantially the same sized structural member. In one steel dome structure designed in accordance with the present invention, substantially all of the arches extending parallel to the skewed axes of symmetry, that is, the arches in sets 56 and 58, were formed of IOWF 49 structural steel members, while the arches in set 52 were formed of substantially all 14 B 26 steel structural members. Thus, a substantial economic savings is achieved because there is very little variation in the type of structural members required for the roof construction.

It is noted, that while each of the above described roof structures, whether formed of rigid arch constructions or of cable supported membranes, have utilized a perimeter ring which lies in a horizontal plane, the ring may in fact have a variety of configurations ane need not be horizontal throughout its entire extent. The only limitation on the configuration of the ring in order to maintain the funicular loading thereof with structural members positioned as discussed above, is that the ring project in plan to a closed curve having skewed axes of symmetry, and preferably that the ends of each individual structural member be on the same horizontal plane. Thus, for example, the ring may take the shape, in a side view, of a curve or catenary or any other type of non-linear configuration so long as the ends of each individual arch are on the same level.

Referring now to FIGS. 7 and 8 of the drawing, there is illustrated a typical joint construction and foundation support for the ring 50 of a steel dome construction formed in accordance with the configuration illustrated in FIG. 6. As seen therein, ring 50 is formed of an I or wide flange beam 90 having vertically extending plates 92 secured thereto, at the point of connection between the ring and the arches. The inside plate 92 has a plate 94 welded thereto and the latter is connected through shear plate 96 by bolts 98 to the arch at the joint. The arch carries the purlins and decking system schematically illustrated at 100 which are secured to the arches in a conventional manner. A peripheral gutter system 102 is also secured to the beam 94 to receive rain, snow and the like from the roof and carry it therefrom.

The base of the beams 90 forming ring 50, at each of the joints between the ring and the arch, are welded to a support plate MM which in turn is welded to a low friction bearing plate 106 having a bearing surface W8. Such a plate may, for example, be formed of a fluorogold slide bearing plate or the equivalent. Plate i106 rests on another bearing plate llltl formed of the same material and having a bearing surface 112. Plate 11th is secured, as by welding, to a support plate lill3 anchored in a concrete foundation 1114 which extends entirely about the periphery of the roof structure. In this manner the ring 50 and roof structure is supported on a concrete foundation and relative movement between the ring and the foundation is permitted in order to avoid the transmission of excessive stresses to the foundation. The bearing plates permit accommodation by the foundation structure of the expansion ad contraction of the roof structure in accordance with temperature changes.

Although illustrative embodiments of the present invention have been described herein with reference to the accompanying drawings, it is to be understood that the invention is not limited to those precise embodiments, and that various changes and modifications may be effected therein by one skilled in the art without departing from the scope or spirit of this invention.

What is claimed is:

ll. A non-circular and non-elliptical roof structure defining an enclosed occupiable building space comprising a ring projecting in plan substantially to a closed curve having major and minor axes and a plurality of skewed axes of symmetry, a plurality of sets relatively rigid arches connected to said ring with the arches of at least two sets respectively extending in plan substantially parallel to two of said skewed axes of symmetry, and another set of arches extending in plan substantially parallel to at least one of said major and minor axes, with the opposite ends of the arches in said another set connected to said ring, said arches in each set crossing the arches in the other sets at predetermined locations throughout said structure and being operatively interconnected to each other at all of said crossing locations, whereby said ring is funicularly loaded under substantially all loading conditions.

2. A roof structure as defined in claim 1 wherein another set of arches extend parallel to the minor axis of said ring.

3. A roof structure as defined in claim ll wherein said another set of arches extend parallel to the major axis of said ring.

4. A roof structure as defined in claim 1 wherein said another set of arches includes two groups of individual arches respectively extending parallel to said major axis and said minor axis.

5. A roof structure as defined in claim 1 wherein said ring is non planar and substantially curved in elevation with the opposed ends of respective arches being located at substantially the same elevation.

6. A roof structure as defined in claim it including a foundation conforming in plan substantially to the closed curve defined by said ring and support plates having frictionally engaged bearing surfaces for supporting said ring on said foundation.

7. A roof structure as defined in claim H wherein said closed curve is selected from a family of closed curves developed by use of the equation (x/a)"' (y/b)" 1, with a and b being different preselected dimensions of the major and minor axes of the curve and the value of m being greater than 2.

8. A roof structure as defined in claim 7 wherein said skewed axis of symmetry coincide with the diagonals of the rectangle circumscribing said closed curve.

9. A roof structure as defined in claim 1 wherein said arches extending paralled to said skewed axes of symmetry intersect and are operatively connected at joints located in plan along lines extending substantially parallel to said major and minor axes and the arches in said another set of arches are respectively located along alternate ones of said lines, the last mentioned arches being operatively connected at the joints along their associated lines to said arches extending parallel to said skewed axis of symmetry to provide a coarse triangulation of structural members within said roof.

110. A roof structure as defined in claim 1 wherein said arches extending parallel to said skewedaxes of symmetry intersect, and are operatively connected at joints located in plan along lines extending substantially parallel to said major and minor axes and the arches in said another set of arches are respectively located along said lines, the last mentioned arches being operatively connected at the joints along their associated lines to said arches extending parallel to said skewed axes of symmetry to provide a fine" triangulation of structural members within said roof.

11. A roof structure as defined in claim 10 wherein the end portions of selected arches, between the last joint along the arch and the ring, are angularly related to the remainder of their associated arch and operatively connected to an adjacent arch at said ring to provide triangulation of structural members along the perimeter of said roof structure.

12. A roof structure as defined in claim 11 wherein said selected arches are selected from said another set of arches.

13. A roof structure as defined in claim 1 including a roof deck secured to said arches to enclose said roof structure.

14. A roof structure defining an enclosed occupiable building space comprising, a peripheral support ring projecting in plan to a closed surve having a plurality of skewed axes of symmetry and developed by the use set of arches extending in plan substantially parallel to l at least one of said major and minor axes, with the opposite ends of said arches in said another set connected to said ring; said arches in each of said sets crossing each other at predetermined locations throughout said structure and being operatively interconnected to each other at substantially all of said crossing locations, and

a roof deck structure mounted on. said arches on the side thereof opposite said occupiable building space, thereby to enclose said arches within said occupiable building space; whereby said ring remains in its closed curved configuration without deformation under substantially all load conditions. 

1. A non-circular and non-elliptical roof structure defining an enclosed occupiable building space comprising a ring projecting in plan substantially to a closed curve having major and minor axes and a plurality of skewed axes of symmetry, a plurality of sets relatively rigid arches connected to said ring with the arches of at least two sets respectively extending in plan substantially parallel to two of said skewed axes of symmetry, and another set of arches extending in plan substantially parallel to at least one of said major and minor axes, with the opposite ends of the arches in said another set connected to said ring, said arches in each set crossing the arches in the other sets at predetermined locations throughout said structure and being operatively interconnected to each other at all of said crossing locations, whereby said ring is funicularly loaded under substantially all loading conditions.
 2. A roof structure as defined in claim 1 wherein another set of arches extend parallel to the minor axis of said ring.
 3. A roof structure as defined in claim 1 wherein said another set of arches extend parallel to the major axis of said ring.
 4. A roof structure as defined in claim 1 wherein said another set of arches includes two groups of individual arches respectively extending parallel to said major axis and said minor axis.
 5. A roof structure as defined in claim 1 wheRein said ring is non-planar and substantially curved in elevation with the opposed ends of respective arches being located at substantially the same elevation.
 6. A roof structure as defined in claim 1 including a foundation conforming in plan substantially to the closed curve defined by said ring and support plates having frictionally engaged bearing surfaces for supporting said ring on said foundation.
 7. A roof structure as defined in claim 1 wherein said closed curve is selected from a family of closed curves developed by use of the equation (x/a)m + (y/b)m 1, with a and b being different preselected dimensions of the major and minor axes of the curve and the value of m being greater than
 2. 8. A roof structure as defined in claim 7 wherein said skewed axis of symmetry coincide with the diagonals of the rectangle circumscribing said closed curve.
 9. A roof structure as defined in claim 1 wherein said arches extending paralled to said skewed axes of symmetry intersect and are operatively connected at joints located in plan along lines extending substantially parallel to said major and minor axes and the arches in said another set of arches are respectively located along alternate ones of said lines, the last mentioned arches being operatively connected at the joints along their associated lines to said arches extending parallel to said skewed axis of symmetry to provide a ''''coarse'''' triangulation of structural members within said roof.
 10. A roof structure as defined in claim 1 wherein said arches extending parallel to said skewed axes of symmetry intersect, and are operatively connected at joints located in plan along lines extending substantially parallel to said major and minor axes and the arches in said another set of arches are respectively located along said lines, the last mentioned arches being operatively connected at the joints along their associated lines to said arches extending parallel to said skewed axes of symmetry to provide a ''''fine'''' triangulation of structural members within said roof.
 11. A roof structure as defined in claim 10 wherein the end portions of selected arches, between the last joint along the arch and the ring, are angularly related to the remainder of their associated arch and operatively connected to an adjacent arch at said ring to provide triangulation of structural members along the perimeter of said roof structure.
 12. A roof structure as defined in claim 11 wherein said selected arches are selected from said another set of arches.
 13. A roof structure as defined in claim 1 including a roof deck secured to said arches to enclose said roof structure.
 14. A roof structure defining an enclosed occupiable building space comprising, a peripheral support ring projecting in plan to a closed surve having a plurality of skewed axes of symmetry and developed by the use of the equation (x/a)m + (y/b)m 1, wherein m equals any number greater than 2 and the values of a and b are different and define major and minor axes in the closed curve; a plurality of sets of rigid arches operatively connected to said ring with the arches of each of said sets extending in plan substantially parallel to a separate one of said skewed axes of symmetry; and an additional set of arches extending in plan substantially parallel to at least one of said major and minor axes, with the opposite ends of said arches in said another set connected to said ring; said arches in each of said sets crossing each other at predetermined locations throughout said structure and being operatively interconnected to each other at substantially all of said crossing locations, and a roof deck structure mounted on said arches on the side thereof opposite said occupiable building space, thereby to enclose said arches within said occupiable building space; whereby said ring remains in its closed curved configuration without deformation under substAntially all load conditions. 